Question

An inventor claims that his engine has the following specifications : 

Temperature limits ...... 750°C and 25°C 

Power developed ...... 75 kW Fuel burned per hour ...... 3.9 kg 

Heating value of the fuel ...... 74500 kJ/kg 

State whether his claim is valid or not.

Answer 1

Temperature of source, T₁ = 750 + 273 = 1023 K 

Temperature of sink, T₂ = 25 + 273 = 298 K 

We know that the thermal efficiency of Carnot cycle is the maximum between the specified temperature limits.

η_carnot = 1 – \(\cfrac{T_2}{T_1}\) = 1 - \(\cfrac{298}{1023}\) = 0.7086 or 70.86%

The actual thermal efficiency claimed,

Since η_thermal > ηcarnot, therefore claim of the inventor is not valid (or possible).